Matrices and Determinants Test

Result

Matrices and Determinants Test - 7

Score
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Weekly Quiz Competition

Question 1
4 / -1

A

B

C

D

Solution
Question 2
4 / -1

A
a³ⁿ

B
a^-3n

C
-a³ⁿ

D
2a³ⁿ

Solution
Question 3
4 / -1

Let M and N are two 3 × 3 non - singular skew-symmetric matrices such that MN = NM. If P^T denotes the transpose of P, then M²N² (M^T N)^-1 (MN^-1)^T is equal to

A
M²

B
- N²

C
- M²

D
MN

Solution
Question 4
4 / -1

If χ is any matrix of order n × p (n and p are integers) and I is an identity matrix of order n × n, then the matrix M = I - χ (χ^' χ)^-1 χ^' is
I. idempotent matrix. II. Mχ = 0

A
I is correct

B
II is correct

C
I is incorrect

D
II is incorrect

Solution
Question 5
4 / -1

If A_3×3 and |A|= 6, then |2adj A| is equal to

A
48

B
8

C
288

D
12

Solution
Question 6
4 / -1

If A is 2 × 2 matrix and |A| = 2, then the matrix represented by |A (adj A)| is equal to

A

B

C

D

Solution
Question 7
4 / -1

If A is non - singular matrix of order 3, then adj (adj A) is equal to

A
A

B
A^-1

C
(1/|A|) A

D
|A| A

Solution
Question 8
4 / -1

Which one of the following is correct always for any two non - singular matrices A and B of same order ?

A
AB = BA

B
(AB)^' = A^' B^'

C
(A + B) (A - B) = A² - B²

D
(AB)^-1 = B^-1 A^-1

Solution
Question 9
4 / -1

A
2

B
3

C
0

D
1

Solution
Question 10
4 / -1

A

B

C

D

Solution